Question

Let the sample mean of a set of 20 data points be 30. If it is discovered that a data point having value 25 was incorrectly entered as 15, what should be the revised value of the sample mean?​

Answer 1

The revised value of the sample mean is 30.5 after correcting the data entry error from 15 to 25 and recalculating the mean.

Step-by-step explanation:

The original sample mean is given as 30 based on 20 data points. If one of the data points was incorrectly entered (15 instead of the actual value of 25), this means the sum of all data points used to calculate the original mean was 10 less than it should have been. To correct this, we simply need to add this 10 back to the total sum and then recalculate the sample mean.

The total sum of the original data points is the sample mean multiplied by the number of data points, which is:
30 x 20 = 600.

To correct the error, we add 10 (the difference between the incorrect entry and the correct value):
600 + 10 = 610.

Now, we divide this corrected total sum by the number of data points to find the revised sample mean:
610 / 20 = 30.5.

Therefore, the revised value of the sample mean is 30.5.